steady state approximation

Examples of steady state approximation in the following topics:

• Steady-State Approximation

  • The steady state approximation can be used to determine the overall rate law when the rate-determining step is unknown.
  • Both cases can be addressed by using what is known as the steady state approximation.
  • With the steady state assumption, we can write the following:
  • We had no knowledge of the rate-determining step, so we used the steady state approximation for our reaction intermediate, N2O2.
  • Simplify overall rate laws using the steady state approximation for reactions with various or unknown rate-limiting steps, explainting the steady state approximation and when it is valid

• Managing the Business Cycle

  • When the economy is not at a steady state, the government and monetary authorities have policy mechanisms to move the economy back to consistent growth.
  • When the economy is not at a steady state and instead is at a point of either overheating (growing to fast) or slowing, the government and monetary authorities have policy mechanisms, fiscal and monetary, respectively, at their disposal to help move the economy back to a steady state growth trajectory.

• Size of the Federal Bureaucracy

  • The size of federal bureaucracy has been steady despite the government's claims of cutting the role of government.
  • State and local government workers are subject to federal mandates.
  • With 16.2 million state and local government workers, the federal government does not need to hire approximately 4.05 million workers to carry out its policies.
  • The Congress and President of the United States delegate specific authority to government agencies to regulate the complex facets of the modern American federal state.
  • In the United States, a number of committees have discussed and debated Red Tape Reduction Acts.

• Electric Charge in the Atom

  • This standard value is equal to approximately 1.6×10-19 Coulombs.
  • Protons have a charge of +1 and a mass of 1 atomic mass unit, which is approximately equal to 1.66×10-24 grams.
  • In the ground state, an atom will have an equal number of protons and electrons, and thus will have a net charge of 0.
  • Atoms in such a state are known as ions.
  • The steady flow of electrons is called current.

• Linear Approximation

  • A linear approximation is an approximation of a general function using a linear function.
  • In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
  • Linear approximations are widely used to solve (or approximate solutions to) equations.
  • Linear approximation is achieved by using Taylor's theorem to approximate the value of a function at a point.
  • Given a twice continuously differentiable function $f$ of one real variable, Taylor's theorem states that:

• The Growth of the Cotton Industry

  • A demand for it already existed in the industrial textile mills in Great Britain, and in time, a steady stream of slave-grown American cotton would also supply northern textile mills.
  • Southern cotton, picked and processed by American slaves, helped fuel the nineteenth-century Industrial Revolution in both the United States and Great Britain.
  • Cotton soon became the primary export in the United States, and by 1860, on the eve of the Civil War, the southern states were providing two-thirds of the world's supply of cotton.
  • The number of slaves rose in concert with the increase in cotton production, increasing from approximately 700,000 in 1790 to roughly 3.2 million in 1850.

• Using Signal Verbs that Fit the Action

  • Stating sequence: first of all, first, firstly, second, secondly, thirdly, fourthly, now, then, next, finally, to complete, after that, last, lastly, furthermore, to begin with, moreover, in addition, to conclude, afterwards
  • Stating purpose: in order to, so that, so as to, to
  • Stating surprise about something unexpected: besides, however, nevertheless, surprisingly, nonetheless, notwithstanding, only, still, while, in any case, at any rate, for all that, after all, at the same time, all the same
  • Approximating results: is just over, is just under, a little over, a little under, about, approximately, nearly
  • Qualifying change: no, minimal, slight, small, slow, gradual, steady, marked, large, dramatic, complete, steep, sharp, rapid, sudden (rise, increase, fluctuation, decrease, decline, reduction, fall, drop, upward trend, downward trend, peak, plateau, level off)

• Architecture of Djenne

  • However, the rise of the Mali Empire in the thirteenth century contributed to its steady decline, and its brief period of dominance came to an end when it was reduced to a tributary state.
  • The rise of Islam witnessed a steady construction of mosques in the region.
  • The central minaret is approximately 48 feet tall.

• Immigration and Illegal Immigration

  • During the 17th century, approximately 175,000 Englishmen migrated to Colonial America.
  • This phenomenon has held true throughout the history of immigration to the United States.
  • In fact, in the United States, only 0.16 percent of the workforce are legal immigrants.
  • An illegal immigrant in the United States is an alien (non-citizen) who has entered the United States without government permission and in violation of United States Nationality Law, or stayed beyond the termination date of a visa, also in violation of the law.
  • Illegal immigrants continue to outpace the number of legal immigrants—a trend that's held steady since the 1990s.

• Half-Life and Rate of Decay; Carbon-14 Dating

  • Libby estimated that the steady-state radioactivity concentration of exchangeable carbon-14 would be about 14 disintegrations per minute (dpm) per gram.
  • Identify the age of materials that can be approximately determined using radiocarbon dating